To the disappointment of some activists, the de Blasio administration’s approach to school integration so far can be summed up in one word: incremental.

However, one small program aimed at diversifying schools in New York City is getting bigger. Last year, seven elementary schools were allowed to change their admissions policies to give disadvantaged students priority for a certain number of seats. All but one of the schools did not have a designated geographic zone. Some of them set aside seats for students who qualified for free or reduced-price lunch, others for students learning English. One gave priority to students in the child welfare system, another to students with family members who are incarcerated.

Now, after the city made an open call for similar admissions proposals, 12 other schools will join the program and initiate their own admissions set-asides. They are a mix of elementary, middle and high schools. Two of the elementary schools, the Charrette School and the East Side School for Social Action, are zoned, so their admissions priorities would go into effect only after all zoned students had been admitted.

In some other cases, the new admissions priority has the potential to reverse a shift in demographics.

The East Village Community School, for instance, a nonzoned elementary school in Manhattan that admits students by lottery, giving priority to students living in District 1, will begin giving priority for half of its prekindergarten and kindergarten seats to students who qualify for free or reduced-price lunch or students who are learning English. The school, which is highly sought after, has seen its students become wealthier in recent years. From 2011-12 to 2015-16, the proportion of its students who qualified for free or reduced-price lunch declined to 21 percent from 36 percent, while the proportion of those learning English declined to 1 percent from 3 percent.

The New American Academy, in Brooklyn, plans to set aside 40 percent of prekindergarten and kindergarten seats for students who qualify for free or reduced-price lunch. Sixty percent of current students in the school qualified in 2015-16, but that was down from 89 percent in 2011-12. The proportion of children learning English fell in the same period, to 2 percent from 5 percent.

Central Park East High School, in Manhattan, plans to set aside 64 percent of seats for students who qualify for free lunch. Currently, 76 percent of students in the school qualify for free lunch, according to the principal, Bennett Lieberman, but he said the proportion had declined in recent entering classes.

“It’s vitally important to me that the school maintain its current level of diversity,” Mr. Lieberman said in a phone interview.

The other schools that will create admissions priorities for disadvantaged students are the Children’s Workshop School, Brooklyn School of Inquiry, East Side Middle School, Math & Science Exploratory School, Middle School 839 and Harvest Collegiate High School.

A version of this article appears in print on , on Page A22 of the New York edition with the headline: 12 More City Schools Enlist in Diversity Initiative. Order Reprints | Today’s Paper | Subscribe